Metamath Proof Explorer

Theorem 19.28v

Description: Version of 19.28 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004)

Ref Expression
Assertion 19.28v ⊢ ∀ x φ ∧ ψ ↔ φ ∧ ∀ x ψ

Proof

Step Hyp Ref Expression
1 19.26 ⊢ ∀ x φ ∧ ψ ↔ ∀ x φ ∧ ∀ x ψ
2 19.3v ⊢ ∀ x φ ↔ φ
3 2 anbi1i ⊢ ∀ x φ ∧ ∀ x ψ ↔ φ ∧ ∀ x ψ
4 1 3 bitri ⊢ ∀ x φ ∧ ψ ↔ φ ∧ ∀ x ψ